Saturday's 1-0 victory over Stoke courtesy of Kevin Mirallas' 70-yard run and finish built on the win over defending Barclays Premier League champions Manchester City before the international break.
The Toffees are now only four points adrift of the top four, and Jagielka said: "We'd like to think we can prolong the chase as long as possible. If we're going into the final game of the season still in with a chance of Champions League football then we have to look at that as a fantastic season."
He went on: "Unfortunately for us it is a season when five or six teams at the top rather than two or three are performing well.
"It seems like Spurs have played well again and won, Arsenal have so everyone seems to be desperate for that fourth spot and we're desperate to be in there as long as possible.
"You can only work with what you are given and I am sure the manager would have loved to have had a lot of money in the January window when we were up there in a better position (they were in the top four in late December) than we are now.
"But it is hard to wish for things which are not going to happen.
"The manager has got the players he's got, he has done the best he has with the players he has got in and when I look around the dressing room I'm happy with the players we have trying to get us into fourth spot.
"We are - as far as spending is concerned - a little bit below the other teams but I am sure they won't look forward to playing us as much as we are looking forward to playing them."
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- Barclays Premier League
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